Решебник по математике 6 класс Виленкин ФГОС Часть 1, 2 Проверочные работы Проверочная работа №1. Повторение

\[\boxed{\mathbf{Проверьте\ себя.\ Страницы\ 136 - 137}}\]

\[\boxed{\mathbf{Проверочная\ работа\ №1.\ Повторение}}\]

\[\boxed{\mathbf{1.}}\]

\[\textbf{а)}\ 6,8 + 2,6 = 9,4\]

\[\textbf{б)}\ 8,4 - 3,7 = 4,7\]

\[\textbf{в)}\ 7,7 \cdot 0,53 = 4,081\]

\[\textbf{г)}\ 67,2\ :0,48 = 6720\ :48 = 140\]

\[\textbf{д)}\ (3,72 + 4,56) + 6,28 =\]

\[= 8,28 + 6,28 = 14,56\]

\[\textbf{е)}\ 4,33 \cdot 7,92 + 4,33 \cdot 2,18 =\]

\[= 4,33 \cdot (7,92 + 2,18) =\]

\[= 4,33 \cdot 10,1 = 43,733\]

\[\boxed{\mathbf{2.}}\]

\[\textbf{а)}\ 82,6 \cdot 0,1 = 8,26\]

\[\textbf{б)}\ 23,14 \cdot 0,25 = 5,785\]

\[\boxed{\mathbf{3.}}\]

\[\textbf{а)}\ 59,5\ :0,4 = 595\ :4 = 148,75\]

\[\textbf{б)}\ 47,4\ :0,16 = 4740\ :16 =\]

\[= 296,25\]

\[\boxed{\mathbf{4.}}\]

\[\textbf{а)}\ 16 = 2 \cdot 2 \cdot 2 \cdot 2;\]

\[12 = 2 \cdot 2 \cdot 3.\]

\[НОД(16;12) = 2 \cdot 2 = 4;\]

\[НОК(16;12) = 2^{4} \cdot 3 = 48.\]

\[\textbf{б)}\ 18 = 2 \cdot 3 \cdot 3;\]

\[24 = 2 \cdot 2 \cdot 2 \cdot 3.\]

\[НОД(18;24) = 2 \cdot 3 = 6;\]

\[НОК(18;24) = 2^{3} \cdot 3^{2} = 72.\]

\[\boxed{\mathbf{5.}}\]

\[\textbf{а)}\ \frac{7}{15} + \frac{3}{10} = \frac{14}{30} + \frac{9}{30} = \frac{23}{30}\]

\[\textbf{б)}\ \frac{7}{15} - \frac{3}{10} = \frac{14}{30} - \frac{9}{30} = \frac{5}{30} = \frac{1}{6}\]

\[\textbf{в)}\ \frac{5}{12} \cdot \frac{9}{20} = \frac{1 \cdot 3}{4 \cdot 4} = \frac{3}{16}\]

\[\textbf{г)}\ \frac{5}{12}\ :\frac{9}{20} = \frac{5}{12} \cdot \frac{20}{9} = \frac{100}{108} = \frac{25}{27}\]

\[\textbf{д)}\ \left( \frac{5}{7} + 3\frac{14}{18} \right) + \frac{2}{7} =\]

\[= \frac{5}{7} + \frac{2}{7} + 3\frac{14}{18} = \frac{7}{7} + 3\frac{14}{18} =\]

\[= 1 + 3\frac{7}{9} = 4\frac{7}{9}\]

\[\textbf{е)}\ 16\frac{19}{40} - \left( 13 + 1\frac{19}{40} \right) =\]

\[= 16\frac{19}{40} - 14\frac{19}{40} = 2\]

\[\boxed{\mathbf{6.}}\]

\[\frac{1}{8} = \frac{125}{1000} = 0,125\]

\[\frac{1}{20} = \frac{5}{100} = 0,05\]

\[\frac{5}{4} = 1\frac{1}{4} = 1\frac{25}{100} = 1,25\]

\[\frac{15}{30} = \frac{1}{2} = \frac{5}{10} = 0,5\]

\[\frac{85}{68} = \frac{5}{4} = 1,25\]

\[\frac{17}{625} = \frac{17 \cdot 16}{10\ 000} = \frac{272}{10000} =\]

\[= 0,0272\]

\[\boxed{\mathbf{7.}}\]

\[1\ сут = 24\ ч;\]

\[24 \cdot \frac{1}{8} = 3\ (ч) - это\ \frac{1}{8}\ суток.\]

\[3\ :\frac{1}{4} = 3 \cdot 4 = 12\ (раз) -\]

\[\frac{1}{4}\ ч\ меньше\ \frac{1}{8}\ суток.\]

\[\boxed{\mathbf{8.}}\]

\[1\ км = 1000\ м.\]

\[1000 \cdot \frac{1}{5} = 200\ (м) - это\ \frac{1}{5}\ км.\]

\[200\ :\frac{1}{10} = 200 \cdot 10 =\]

\[= 2000\ (раз) -\]

\[\frac{1}{5}\ км\ больше\ \frac{1}{10}\ м.\]

\[\boxed{\mathbf{9.}}\]

\[\textbf{а)} - 4 + 1,3 = - 2,7\]

\[\textbf{б)} - 5,6 - ( - 8) = - 5,6 + 8 =\]

\[= 2,4\]

\[\textbf{в)} - 6\frac{3}{4} - ( - 0,75) =\]

\[= - 6,75 + 0,75 = - 6\]

\[\textbf{г)} - 0,3 \cdot ( - 0,3) = 0,09\]

\[\textbf{д)} - 5 \cdot 20 = - 100\]

\[\textbf{е)}\ 2\frac{3}{4} \cdot ( - 3,7) \cdot 0 = 0\]

\[\textbf{ж)}\ ( - 42)\ :6 = - 7\]

\[\textbf{з)} - 36\ :( - 0,6) = 360\ :6 = 60\]

\[\textbf{и)}\ \left( - 12\frac{3}{11} \right)\ :( - 3) = \frac{135}{11} \cdot \frac{1}{3} =\]

\[= \frac{45}{11} = 4\frac{1}{11}\]

\[\boxed{\mathbf{10.}}\]

\[\textbf{а)}\ |27,8| - | - 27,8| =\]

\[= 27,8 - 27,8 = 0\]

\[\textbf{б)}\ \left| \frac{7}{9} \right| \cdot \left| - 2\frac{1}{4} \right| = \frac{7}{9} \cdot \frac{9}{4} =\]

\[= \frac{7}{4} = 1\frac{3}{4}\]

\[\textbf{в)}\ 0,36\ :| - 0,18| = 0,36\ :0,18 =\]

\[= 36\ :18 = 2\]

\[\boxed{\mathbf{11.}}\]

\[\textbf{а)}\ Да;\]

\[\textbf{б)}\ да.\]

\[\boxed{\mathbf{12.}}\]

\[4,5\ дм = 45\ см;0,4\ м = 40\ см.\]

\[V = abc = 12 \cdot 45 \cdot 40 =\]

\[= 480 \cdot 45 = 21600\ см^{3} =\]

\[= 21,6\ дм^{3}\text{.\ }\]

\(Ответ:21,6\ дм^{3}.\)